Question at position 12 [1−134][025−3]=\begin{bmatrix} 1 & -1 \ 3 & 4 \end{bmatrix} \begin{bmatrix} 0 & 2 \ 5 & -3 \end{bmatrix} =[−5520−6]\begin{bmatrix} -5 & 5 \ 20 & -6 \end{bmatrix}[68−4−17]\begin{bmatrix} 6 & 8 \ -4 & -17 \end{bmatrix}[−2838]\begin{bmatrix} -2 & 8 \ 3 & 8 \end{bmatrix}[4−106]\begin{bmatrix} 4 & -1 \ 0 & 6 \end{bmatrix}[0−215−12]\begin{bmatrix} 0 & -2 \ 15 & -12 \end{bmatrix}

Question

Question at position 12 [1−134][025−3]=\begin{bmatrix} 1 & -1 \ 3 & 4  \end{bmatrix} \begin{bmatrix} 0 & 2  \ 5 & -3 \end{bmatrix} =[−5520−6]\begin{bmatrix} -5 & 5 \ 20 & -6 \end{bmatrix}[68−4−17]\begin{bmatrix} 6 & 8  \ -4 & -17 \end{bmatrix}[−2838]\begin{bmatrix} -2 & 8 \ 3 & 8  \end{bmatrix}[4−106]\begin{bmatrix} 4 & -1 \ 0 & 6  \end{bmatrix}[0−215−12]\begin{bmatrix} 0 & -2 \ 15 & -12 \end{bmatrix}

BlackTom AI · Accepted Answer

To tackle this problem, I will restate the given sequence and then examine each candidate option in turn, explaining what each represents and why it does or does not match.

- The question begins with a chain of matrix multiplications: (1  -1; 3  4) times (0  2; 5 -3) equals something. When you multiply the two 2x2 matrices, you compute each entry of the product:
  - Top-left entry: 1*0 + (-1)*5 = -5
  - Top-right entry: 1*2 + (-1)*(-3) = 2 + 3 = 5
  - Bottom-left entry: 3*0 + 4*5 = 0 + 20 = 20
  - Bottom-right entry: 3*2 + 4*(-3) = 6 - 12 = -6
  So the product is the 2x2 matrix [ [-5, 5], [20, -6] ].

Option analysis:
- Option 1 displays the sequence:
  [
  −
  5
  	
  5

20
  	
  −
  6
  ]
  This corresponds to the four numbers -5, 5, 20, -6 written in a column (a 4x1 vector). This matches exactly the four entries obtained from the first multiplication (top-left, top-right, bottom-left, bottom-right) arranged in the same order. Since the initial multiplication result is [-5, 5; 20, -6], placing those entries in the same sequence as a column yields [-5, 5, 20, -6]. Therefore Option 1 is consistent with the computed first-step result.

- Option 2 shows the sequence:
  [
  6
  	
  8

−
  4
  	
  −
  17
  ]
  This corresponds to the numbers 6, 8, -4, -17 arranged as a 4x1 column, which do not match the first-step product we just computed. Since the first multiplication already produced -5, 5, 20, -6, this option diverges immediately from the actual result of the first multiplication.

- Option 3 shows:
  [
  −
  2
  	
  8

3
  	
  8
  ]
  Here the numbers are -2, 8, 3, 8. These values do not align with the computed first-step results (-5, 5, 20, -6). Unless additional steps were performed to transform the result into this specific column, this option cannot be correct given the verified first product.

- Option 4 shows:
  [
  4
  	
  −
  1

0
  	
  6
  ]
  The numbers 4, -1, 0, 6 do not match the initial product’s entries (-5, 5, 20, -6). This mismatch indicates this option does not reflect the immediate result of the multiplication we computed first.

- Option 5 shows:
  [
  0
  	
  −
  2

15
  	
  −
  12
  ]
  The values 0, -2, 15, -12 are again not consistent with the -5, 5, 20, -6 result from the first multiplication, so this option cannot be the correct continuation from the initial step.

Summary:
- The only option that matches the explicit first-step product [-5, 5; 20, -6] when represented as a column vector is Option 1. The other options present different numbers that do not correspond to the initial multiplication result, hence are inconsistent with the computation shown at the outset.
- If one were to continue the chain of multiplications beyond the first step, one would need to perform additional matrix products as indicated in the problem statement; however, the question’s answer choices appear to test recognition of the immediate first-step result, which Option 1 correctly captures.

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希望你的学习变得更简单

Vector a = 10 12 And vector b = 2 3 Whats the value of ab ? ( is matrix multiplication); Please enter a number with no decimals.